Add dynamic footer badge marquee with admin management.

Store badges in Postgres, expose public/admin APIs, render an infinite footer slider, and ship /admin for paste-embed CRUD.

prisma/schema.prisma

@@ -189,3 +189,21 @@ model JobItem {
   youtubeVideoId    String?
   error             String?
 }
+
+/// Site footer badge / launch-directory embeds (managed via /admin)
+model FooterBadge {
+  id        String   @id @default(cuid())
+  name      String
+  /// Raw paste from Product Hunt / LaunchBuff / etc. (preferred source)
+  embedHtml String?  @db.Text
+  /// Parsed or manually set image URL (used when embedHtml is empty)
+  imageUrl  String?
+  /// Parsed or manually set destination URL
+  linkUrl   String?
+  isActive  Boolean  @default(true)
+  sortOrder Int      @default(0)
+  createdAt DateTime @default(now())
+  updatedAt DateTime @updatedAt
+
+  @@index([isActive, sortOrder])
+}